Question 35 of 36intermediate🔧 ApplyShort Answer3 marks

Which of the following numbers are divisible by all of 2, 4, 5, 8 and 10: 572, 2352, 5600, 6000, 77622160.

Correct Answer

Divisibility Rules: For divisibility by all these numbers, the number must:

  • End in 0 (for 5 and 10)
  • Be even (for 2)
  • Have last two digits divisible by 4
  • Have last three digits divisible by 8

Step 1: Check 572 Ends in 2 Not divisible by 5 or 10 ∴ Not divisible by all

Step 2: Check 2352 Ends in 2 Not divisible by 5 or 10 ∴ Not divisible by all

Step 3: Check 5600 Ends in 0 Last two digits 00 divisible by 4 Last three digits 600 divisible by 8 (600 ÷ 8 = 75) ∴ Divisible by all

Step 4: Check 6000 Ends in 0 Last two digits 00 divisible by 4 Last three digits 000 divisible by 8 ∴ Divisible by all

Step 5: Check 77622160 Ends in 0 Last two digits 60 divisible by 4 Last three digits 160 divisible by 8 (160 ÷ 8 = 20) ∴ Divisible by all

Answer: 5600, 6000, and 77622160

Exercise: Figure it Out (Section 6) | Q: 6 | (Page Page 20)
For More Understanding

Explanation

For divisibility by all these numbers, the number must: end in 0 (for 5 and 10), be even (for 2), have last two digits divisible by 4, and have last three digits divisible by 8. 572: ends in 2, not divisible by 5. 2352: ends in 2, not divisible by 5. 5600: ends in 0, last two digits 00 divisible by 4, last three digits 600 divisible by 8. 6000: ends in 0, last three digits 000 divisible by 8. 77622160: ends in 0, last three digits 160 divisible by 8.

Solution Steps

  1. Step 1: Check 572: Ends in 2, not divisible by 5 or 10.

  2. Step 2: Check 2352: Ends in 2, not divisible by 5 or 10.

  3. Step 3: Check 5600: Ends in 0. Last two digits 00 divisible by 4. Last three digits 600 divisible by 8 (600÷8=75). Divisible by all.

  4. Step 4: Check 6000: Ends in 0. Last two digits 00 divisible by 4. Last three digits 000 divisible by 8. Divisible by all.

  5. Step 5: Check 77622160: Ends in 0. Last two digits 60 divisible by 4. Last three digits 160 divisible by 8 (160÷8=20). Divisible by all.

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